Let the side of an equilateral triangle be ‘a’ 
  Area   $=\frac{\sqrt{3}{\mathrm{a}}^2}{4}=\mathrm{S}\text{ sq. }\mathrm{cm}$
   ${\mathrm{a}}^2=\frac{4\mathrm{S}}{\sqrt{3}}$    ......(i)
Now the length of wire =     
= perimeter of triangle                 

= perimeter of circle
⇒   3a    = 2πr
$\Rightarrow \mathrm{r}=\frac{3\mathrm{a}}{2\mathrm{\pi }}$ 
 Then area of circle
${\mathrm{\pi r}}^2=\mathrm{\pi }{\left(\frac{3\mathrm{a}}{2\mathrm{\pi }}\right)}^2$     .....(ii)
 put the value of from equation (i)
 ${\mathrm{\pi r}}^2=\frac{3\sqrt{3}\mathrm{S}}{\mathrm{\pi }}$